通过惩罚邻近选择进行大数据集的克里金法
Kriging for large datasets via penalized neighbor selection
AI总结：
本文提出一种基于惩罚的克里金方法，通过数据驱动的邻近选择提升大空间数据集的预测效率与准确性。
摘要：
克里金法是空间预测的基本工具，但其计算复杂度为O(N^3)，对于大数据集来说变得不可行。尽管局部克里金法使用K-最近邻来解决这个问题，但K的选择通常依赖于随意的标准，无法考虑空间相关结构。我们提出了一种惩罚克里金框架，将LASSO型惩罚直接纳入克里金方程中，以实现自动、数据驱动的邻近选择。我们进一步将此扩展到自适应LASSO，使用数据驱动的惩罚权重，以考虑空间相关结构。我们的方法通过ℓ1正则化确定哪些观测值贡献非零权重，惩罚参数通过基于有效样本量的新标准选择，以平衡预测精度与信息冗余。数值实验表明，惩罚克里金法自动适应空间相关结构，选择更少的邻居用于平滑过程，更多邻居用于高度变化的领域，同时在显著降低计算成本的情况下保持与全局克里金法相当的预测精度。
英文摘要：
Kriging is a fundamental tool for spatial prediction, but its computational complexity of $O(N^3)$ becomes prohibitive for large datasets. While local kriging using $K$-nearest neighbors addresses this issue, the selection of $K$ typically relies on ad-hoc criteria that fail to account for spatial correlation structure. We propose a penalized kriging framework that incorporates LASSO-type penalties directly into the kriging equations to achieve automatic, data-driven neighbor selection. We further extend this to adaptive LASSO, using data-driven penalty weights that account for the spatial correlation structure. Our method determines which observations contribute non-zero weights through $\ell_1$ regularization, with the penalty parameter selected via a novel criterion based on effective sample size that balances prediction accuracy against information redundancy. Numerical experiments demonstrate that penalized kriging automatically adapts neighborhood structure to the underlying spatial correlation, selecting fewer neighbors for smoother processes and more for highly variable fields, while maintaining prediction accuracy comparable to global kriging at substantially reduced computational cost.
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